Final answer:
To determine a linear equation, find the slope 'm' from two points on the line, then use one of those points to solve for 'b', the y-intercept. Plotting the function on a graph requires both 'b' and 'm' to draw the line correctly.
Step-by-step explanation:
To determine the full equation of a linear function, we need to establish values for 'b' and 'm' in the equation y = b + mx, where 'm' is the slope of the line and 'b' is the y-intercept. The slope 'm' can be calculated if we know two points on the line since the slope is the change in y over the change in x (rise over run). Once the slope is known, and with at least one point on the line (x, y), we can plug these values into the equation to solve for 'b', the y-intercept. If the linear equation has to be determined from a word problem or a set of data points, we first extract the known values, identify what we need to solve for, and then select the appropriate equation to determine the unknowns.
To express equations graphically, plot the linear function on a coordinate plane using the y-intercept and slope. The intercept 'b' tells us where the line crosses the y-axis, and the slope 'm' dictates the angle of the line as it moves through the plane.